The present invention relates to a power transfer device and a control method thereof, and a lock-up clutch device, and in particular to a power transfer device including a stepped automatic transmission mounted on a vehicle to transfer power from a power source to an axle using changeable shift speeds and a control method thereof, and a lock-up clutch device including a lock-up clutch mounted on a vehicle to engage and disengage an input-side fluid transmission element connected to a power source and an output-side fluid transmission element connected to an input shaft of a stepped automatic transmission.